Integrated mask process modeling for better yield predictions

Conventional lithography simulation often treats mask manufacturing as an ideal process that introduces no distortions, which leads to inaccurate patterning and yield predictions since the mask making process introduces distortions. Approaches to model the distortions from the mask process and their corrections often take a black-box form, which limits the capabilities of end-to-end modeling, disallowing integrated lithography simulations and mask-aware process corrections. The aim of this work is to develop efficient and differentiable "white-box" models for the mask process that help yield prediction and improve design for manufacturability through enabling end-to-end optimization. Our approach involves pre-processing SEM images of the manufactured mask and converting them into a raster format to allow differentiable pixel loss formulations. We then fit a mask process from mask input design to manufactured SEM using accurate machine learning models. We illustrate that such mask process model can be integrated in end-to-end lithography simulations to improve the accuracy of wafer pattern predictions with minimal overhead and can be used for efficient sensitivity analysis of the mask. Moreover, the utilization of differentiable modeling for all process steps including the mask process is instrumental in enabling effective end-to-end lithography modeling and optimization.